SVEN THOMMESEN FINANCE 2400/3610/3700 SELECTED FORMULAS FOR CERTAIN FINANCIAL RELATIONSHIPS [From Floyd and Allen’s Real Estate Principlesand other sources] VARIABLES USED IN THE FOLLOWING PAGES: N = the number of periods (months, years) I/YR = the applicable interest rate (% per year) PV = Present Value (value of a project at an early point in time) FV = Future Value (value of a project at a later point in time) PMT = Payment (the size of the recurring cash flow associated with the project) BEG = Begin Mode (used to set the calculator to expect an Annuity Due) END = End Mode (used to set the calculator to expect a Normal Annuity) P/YR = Payments Per Year (or in some cases, compounding periods per year) PVA = Present value of an annuity FVA = Future value of an annuity SFP = Sinking fund payment

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FUTURE VALUE OF A SINGLE PAYMENT [LUMP SUM] EXPLANATION: The future value of a lump sum is the value the lump sum would grow to, if left to earn interest at a given rate over a specific time period, with no further contributions from the saver/investor. BASIC FORMULA: (1)nFVPViEXAMPLE: You save $2,500 and leave it for 12 years at 7% interest. How much do you have? SOLUTION USING THE FORMULA: FV = $2,500.00 * (1 + 0.07)^12 = $5,630.48 SOLUTION USING THE TABLES: LOOK UP FVF(12 YEARS, 7%) = 2.252 FV = PV * FV-FACTOR = $2,500.00 * 2.252 = $5,630.00 SOLUTION USING THE FINANCIAL CALCULATOR: BEG/END = END [regular annuity: interest added at end of each period] P/YR = 1 [interest added once a year] CLEAR [get rid of old data] N = 12 [# periods] I = 7 [interest rate in %] PV = -2,500.00 [deposit at start; note the sign!] PMT = 0 [no recurring payments here] Solve for FV -> $5,630.4790 [amount available at end]

PRESENT VALUE OF A SINGLE PAYMENT [LUMP SUM] EXPLANATION: The (discounted) present value is the answer to how much a future sum of money is worth in terms of today’s dollars. Or, if you will, how much you would have to deposit in the bank today in order to have a specific sum available (with interest) at a future date. BASIC FORMULA: (1)nFVPViEXAMPLE: You find a savings account which your parents started for you 15 years ago containing $7,600.00. The money has been earning 5% interest over that time. How much did your parents deposit back then? SOLUTION USING THE FORMULA: 157,600.003,655.73)(1.05)nFVPViSOLUTIONS USING THE TABLES: Look up the present value of $1 at 5% over 15 years: PVF(15 years, 5%) = .4810 Then: PV = FV * PVF = $7,600.00 * .4810 = $3,655.60 Alternatively, we can look up the future value factor: FVF(15 years, 5%) = 2.0789 Then: PV = FV / FVF = $7,600.00 / 2.0789 = $3,655.78 SOLUTION USING THE FINANCIAL CALCULATOR:

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